Strategy guides › Fold
How to solve Fold: read the target backwards, and trust the backs
▶ Play Fold🎯 Try a sheet with only one good first fold
The target is two cells: Rings and Flower. The strip in front of you has six cells, and none of them shows Rings on its face. Halving the strip and folding once more gets it down to two cells in two folds, and it looks like the obvious plan. On this sheet the best it can do is Flower and Rings: the right prints, the wrong way round. Par is three.
That gap between “small enough” and “right” is the whole game. Here is how to close it.
Two rules, and what they really mean
Tap a crease and the shorter side turns over onto the longer side. On the middle crease, the left (or the top) half turns. Only the top print of each stack counts. That’s all the code does.
Two consequences follow, and they are worth saying out loud. First, a turned flap lands face down, so what you see on it afterwards is the back of whatever was at the bottom of that flap. Second, turning a stack over reverses it: its bottom layer becomes its top. A cell that has been turned once shows its back; turned twice, its front again.
Shrinking fast is not the same as matching
The size of the target tells you how small the sheet has to get, and the quickest way to get there is to halve. But we ran our own solver over 600 sheets per level and compared par with the fewest folds the size alone needs. On Easy, par is longer than the size alone needs on 62% of sheets. On Normal it’s 57%. On Hard it’s every sheet, because the level only keeps sheets that need four or five folds.
So the habit to build is this: when the target is two cells wide and the sheet is six, don’t ask “how do I get to two?” Ask “which two cells, which way up, end on top?”
Nearly everything you need is on the back
This one surprised us. When the solver’s par route is finished, how many of the visible prints are a cell’s front? On Easy, 23%. On Normal, 5%. On Hard, 2%. Almost every print in the target is the back of some cell, sitting face down on top of a stack.
That is just what folding does: every fold puts backs on top, and the only way to bring a front back up is to turn the same stack twice. So before your first fold, press “See the back” and look for the target’s prints there. If Rings only exists on the back of cell 1, then cell 1 has to be turned an odd number of times and end on top.
One thing to remember when you look: the back view is mirrored, exactly like turning a real sheet over. The cell on the far left is now on the far right.
Plan from the last fold
The last fold decides the top of every spot it covers. Whatever was at the bottom of the flap ends up on top, turned over. So look at the target and ask which cells could have arrived last.
In the figure, the right-hand spot of the target is Flower, and the only Flowers on the sheet are the back of cell 4 and the fronts of cells 4 and 5. For it to show, cell 4 has to arrive on top back up, on the very last fold. Work back from there: before that fold, cell 4 must be at the bottom of the end spot, face up. The first fold never touches it, and the second only lays cell 5 on top of it.
Order matters in two dimensions too. We took 2,000 random four-fold sequences on a 4 by 4 sheet with folds in both directions and played them again with every fold along a horizontal crease done first. The picture on top changed in 56% of them. Folding up and down, then across, is not the same as across, then up and down.
How many good first folds there are
On average, a Normal sheet has five creases at the start and only two of them begin a par route; on Hard, six creases and fewer than three good ones. Easy sits in between, 1.7 good first folds out of five. Fold counts every fold, and undo does not refund one, so the first tap is the most expensive mistake. On Normal 71% of sheets have a par of 3 and the rest 4; on Hard 84% are 4 and 16% are 5.
A method that works
- Read the target’s size, and which way the sheet has to shrink.
- Find each target print on the sheet, front and back.
- Pick the cell that has to end on top of each spot, and count whether it needs to be turned an odd or even number of times.
- Choose the last fold first, then work back.
Practice
The practice sheet is Normal and needs four folds. Only one of its five creases starts a par route, and it is not the one that shrinks the sheet the fastest. Look at the backs before you tap anything.
